CYCLUS
uniform_taylor.h
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1 #ifndef CYCLUS_SRC_UNIFORM_TAYLOR_H_
2 #define CYCLUS_SRC_UNIFORM_TAYLOR_H_
3
4 #include <boost/lexical_cast.hpp>
5
6 #include "use_matrix_lib.h"
7
8 namespace cyclus {
9
10 /// @class UniformTaylor
11 ///
12 /// A class that solves the matrix exponential
13 /// problem using the Taylor Series with Uniformization method.
15  public:
16  /// Solves the matrix exponential problem:
17  ///
18  /// dx(t)
19  /// ----- = A * x(t)
20  /// dt
21  ///
22  /// where A is an nxn Matrix and x(t) is a nx1 Vector. The solution
23  /// to this equation can be determined by calculating:
24  ///
25  /// x(t) = e^(tA) * x(t=0)
26  ///
27  /// @param A the Matrix
28  /// @param x_o the initial condition Vector x(t=0)
29  /// @param t the value for which the solution is being evaluated
30  /// @return the solution Vector x(t)
31  /// @throw <string> if the Uniform Taylor method cannot be used
32  static Vector MatrixExpSolver(const Matrix& A, const Vector& x_o,
33  const double t);
34
35  private:
36  /// Returns the diagonal element in the Matrix A
37  /// that has the largest absolute value.
38  ///
39  /// @param A the Matrix
40  /// @return the diagonal element of A with the largest absolute value
41  static double MaxAbsDiag(const Matrix& A);
42
43  /// Computes the solution Vector x_t using the Taylor Series with
44  /// Uniformization method.
45  ///
46  /// @param B the Matrix B = A + alpha * I
47  /// @param x_o the initial condition Vector
48  /// @param alpha the diagonal element of A with the largest absolute value
49  /// @param t the value for which the solution is being evaluated
50  /// @param tol the accuracy desired
51  /// @return the solution Vector x_t for the given value of t
52  /// @throw <string> if exp(-alpha * t) or exp(alpha * t) exceeds range
53  static Vector GetSolutionVector(const Matrix& B, const Vector& x_o,
54  double alpha, double t, double tol);
55
56  /// Computes the maximum number of terms needed to obtain an accuracy
57  /// of epsilon when using the Taylor Series with Uniformization
58  /// method.
59  /// @param alpha_t the product alpha * t
60  /// @param epsilon the accuracy desired in the series computation
61  /// @return the maximum number of terms needed
62  /// @throw <string> if exp(alpha * t) exceeds range
63  static int MaxNumTerms(long double alpha_t, double epsilon);
64 };
65
66 } // namespace cyclus
67
68 #endif // CYCLUS_SRC_UNIFORM_TAYLOR_H_
struct pyne::alpha alpha
a struct matching the &#39;/decay/alphas&#39; table in nuc_data.h5.
A class that solves the matrix exponential problem using the Taylor Series with Uniformization method...
static Vector MatrixExpSolver(const Matrix &A, const Vector &x_o, const double t)
Solves the matrix exponential problem:
taken directly from OsiSolverInterface.cpp on 2/17/14 from https://projects.coin-or.org/Osi/browser/trunk.
Definition: agent.cc:14